AMechanically
Verified,
Efficient,
Sound
and
Complete
Theorem
Prover
For
First
Order
Logic

Title:

A Mechanically Verified, Efficient, Sound and Complete Theorem Prover For First Order Logic

Author:

Tom Ridge

Submission date:

2004-09-28

Abstract:

Soundness and completeness for a system of first order logic are formally proved, building on James Margetson's formalization of work by Wainer and Wallen. The completeness proofs naturally suggest an algorithm to derive proofs. This algorithm, which can be implemented tail recursively, is formalized in Isabelle/HOL. The algorithm can be executed via the rewriting tactics of Isabelle. Alternatively, the definitions can be exported to OCaml, yielding a directly executable program.